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Deriving Functions for Pareto Optimal Fronts Using Genetic Programming

  • Armand Maree
  • Marius Riekert
  • Mardé HelbigEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10841)

Abstract

Genetic Programming is a specialized form of genetic algorithms which evolve trees. This paper proposes an approach to evolve an expression tree, which is an N-Ary tree that represents a mathematical equation and that describes a given set of points in some space. The points are a set of trade-off solutions of a multi-objective optimization problem (MOOP), referred to as the Pareto Optimal Front (POF). The POF is a curve in a multi-dimensional space that describes the boundary where a single objective in a set of objectives cannot improve more without sacrificing the optimal value of the other objectives. The algorithm, proposed in this paper, will thus find the mathematical function that describes a POF after a multi-objective optimization algorithm (MOA) has solved a MOOP. Obtaining the equation will assist in finding other points on the POF that was not discovered by the MOA. Results indicate that the proposed algorithm matches the general curve of the points, although the algorithm sometimes struggles to match the points perfectly.

Keywords

Multi-objective optimization Pareto optimal front Genetic programming 

Notes

Acknowledgements

This work is based on the research supported by the National Research Foundation (NRF) of South Africa (Grant Number 46712). The opinions, findings and conclusions or recommendations expressed in this article is that of the author(s) alone, and not that of the NRF. The NRF accepts no liability whatsoever in this regard.

References

  1. 1.
    Konak, A., Coit, D.W., Smith, A.E.: Multi-objective optimization using genetic algorithms: a tutorial. Reliab. Eng. Syst. Saf. 91(9), 992–1007 (2006)CrossRefGoogle Scholar
  2. 2.
    Ganesan, T., Elamvazuthi, I., Vasant, P.: Multiobjective design optimization of a nano-CMOS voltage-controlled oscillator using game theoretic-differential evolution. Appl. Soft Comput. 32, 293–299 (2015)CrossRefGoogle Scholar
  3. 3.
    Shirazi, A., Najafi, B., Aminyavari, M., Rinaldi, F., Taylor, R.A.: Thermal-economic-environmental analysis and multi-objective optimization of an ice thermal energy storage system for gas turbine cycle inlet air cooling. Energy 69, 212–226 (2014)CrossRefGoogle Scholar
  4. 4.
    Courteille, E., Mortier, F., Leotoing, L., Ragneau, E.: Multi-objective robust design optimization of an engine mounting system. Technical report, SAE Technical Paper (2005)Google Scholar
  5. 5.
    Deb, K., Sundar, J.: Reference point based multi-objective optimization using evolutionary algorithms. In: Proceedings of the 8th Annual Conference on Genetic and Evolutionary Computation, pp. 635–642. ACM (2006)Google Scholar
  6. 6.
    Marler, R.T., Arora, J.S.: Survey of multi-objective optimization methods for engineering. Struct. Multidiscip. Optim. 26(6), 369–395 (2004)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Wang, F., Lai, X., Shi, N.: A multi-objective optimization for green supply chain network design. Decis. Support Syst. 51(2), 262–269 (2011)CrossRefGoogle Scholar
  8. 8.
    Giacomelli, D.: Geneticsharp. https://github.com/giacomelli/GeneticSharp. Accessed 02 Feb 2018
  9. 9.
    Ferreira, C.: Gene expression programming in problem solving. In: Roy, R., Köppen, M., Ovaska, S., Furuhashi, T., Hoffmann, F. (eds.) Soft Computing and Industry, pp. 635–653. Springer, London (2002).  https://doi.org/10.1007/978-1-4471-0123-9_54CrossRefGoogle Scholar
  10. 10.
    Banzhaf, W., Nordin, P., Keller, R.E., Francone, F.D.: Genetic Programming: An Introduction, vol. 1. Morgan Kaufmann, San Francisco (1998)CrossRefGoogle Scholar
  11. 11.
    Engelbrecht, A.P.: Computational Intelligence: An Introduction. Wiley, Hoboken (2007)CrossRefGoogle Scholar
  12. 12.
    Koza, J.R.: Genetic Programming: On the Programming of Computers by Means of Natural Selection, vol. 1. MIT Press, Cambridge (1992)zbMATHGoogle Scholar
  13. 13.
    Miller, B.L., Goldberg, D.E., et al.: Genetic algorithms, tournament selection, and the effects of noise. Complex Syst. 9(3), 193–212 (1995)MathSciNetGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of PretoriaPretoriaSouth Africa

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